1. Field of the Invention
The present invention relates to a function transform apparatus for transforming a function in one domain into a function in another domain, and particularly, to a two-dimensional inverse discrete cosine transform (I-DCT) apparatus which is used to reproduce an image from a two-dimensional discrete cosine transform (DCT) of the image.
2. Description of the Related Art
A two-dimensional discrete cosine transform (DCT) efficiently compresses and encodes image data. The DCT is widely adopted for encoding and compressing images in visual telephone systems based on ITU-T Recommendation H.261, dynamic images in MPEG (Moving Picture Experts Group) systems, and static images in JPEG (Joint Photographic Experts Group) systems. To decode the DCT-encoded images, a two-dimensional inverse discrete cosine transform (I-DCT) is used. The I-DCT changes a two-variable function in a frequency domain into a two-variable function in a positional variable domain. A microprocessor or a DSP must carry out the I-DCT at a high speed, to provide an inexpensive compact image decoder.
An example of a technique for speedily executing the I-DCT is a Chen algorithm, which carries out an 8-by-8 I-DCT operation with 416 additions and 256 multiplications.
A microprocessor or a DSP employing the Chen algorithm to carry out the I-DCT, however, does not have sufficient operation speed. The Chen algorithm is impractical to decode dynamic images because it provides an insufficient frame rate.
DCT-encoded data includes DCT coefficients for two-dimensional discrete vertical and horizontal spatial frequencies. The DCT coefficients are usually quantized to compress the data. Therefore, the DCT coefficients to be transmitted or stored have the following characteristics:
(1) When encoded at a compression ratio that secures a practical image quality, about 1/8 of the DCT coefficients are non-zero coefficients and the remaining 7/8 are zero. PA1 (2) Most of the non-zero coefficients are around zero. PA1 (3) Due to quantization, only certain coefficients, of the possible DCT coefficients, occur. PA1 (4) DCT coefficients for two-dimensional spatial frequencies may be numbered in a zigzag manner in a two-dimensional plane and transformed into a one-dimensional sequence of numbers. The sequence of numbers is transformed into a combination of a zero run length indicating the length of consecutive zeroes and the level of a non-zero DCT coefficient that follows the consecutive zeroes, and such combinations are transmitted or stored.
The Chen algorithm may improve the operation speed of the I-DCT operation on general functions but it does not utilize the above-mentioned characteristics of DCT coefficients.